Inverse Sine

In previous courses, you've learned about Functions and their Inverses.

Here are some important points to review:

An inverse relation switches the input and output!
An inverse relation is a function if the original function is one-to-one.
In a one-to-one function each y-value is paired with exactly one x-value.

Watch this video to get an idea of how we will restrict the domain of equation image indicator $LaTeX: f\left(x\right)=\sin x\:to\:create\:f^{\:-1}\left(x\right)=\sin^{-1}x$ .

So, now that you understand where equation image indicator $LaTeX: f\left(x\right)=\sin^{-1}x$ is. It is important to know some of these facts:

We can call the inverse function $LaTeX: f\left(x\right)=\sin^{-1}x\:or\:f\left(x\right)=arc\:\sin x$ .
The domain of $LaTeX: f\left(x\right)=\sin^{-1}x$ is [-1, 1].
The range of $LaTeX: f\left(x\right)=\sin^{-1}x\:is\:\left[-\frac{\Pi}{2},\:\frac{\Pi}{2}\right]$

inverse sine cycle
sine(angle)=ratio
sine to -1(ratio)=angle
The input becomes the output
the output becomes the input

image of a sine unit circle indicating positive sine and negative sine

Watch this video to practice a few more problems:

Try these problems to check your understanding:

IMAGES CREATED BY GAVS